Badge style is broken when filtered to less than three

Short answer

A fixed max-height rule is at the heart of the issue. In the 6 to 8 weeks it takes to fix this, you can use the following overrides (apologies for using !important, but since SE's rulesets also use it, there is no other way):

.popup._badge-selection {
  /* prevents vertical centering of the container */
  justify-content: start !important;
}

.popup._badge-selection .-list-item {
  /* removes content overflow */
  max-height: unset !important;
}

.popup .js-badge-list-container {
  /* keeps badge horizontal alignment */
  justify-content: center;
  /* removes badge vertical stretch */
  height: unset !important;
}

If anyone needs a quick JavaScript snippet, here it is:

((_w, d) => {
  const style = d.createElement("style");
  d.head.append(style);
  const { sheet } = style;
  if (!sheet) return;
  [
    `.popup._badge-selection {
            justify-content: start !important;
        }`,
    `.popup._badge-selection .-list-item {
            max-height: unset !important;
            min-width: 256px;
        }`,
    `.popup .js-badge-list-container {
            justify-content: center;
            height: unset !important;
        }`,
  ].forEach(rule => sheet.insertRule(rule));
})(window, document);

Long answer

As the badge container can grow indefinitely, at some point the wrapped description text (which also has padding-top and padding-bottom of 16px and 12px respectively) starts to overflow the container. Here is an extract from the ruleset:

.popup._badge-selection .-list-item {
  /* ...other rules */
  max-height: 128px;
}

Simply removing the rule would've solved the problem if not for the inline height: 75% set on the parent container, which makes an unrestrained badge container stretch the full height of the parent leading to:

One could add the ai-start class to prevent the flex item from stretching, but this obviously messes up the tile layout of multiple badges:

Another difficulty is presented by the fact badge filtering also uses inline styles (display: none <-> display: block) to show/hide badges depending on the query and not the Stacks classes (d-none and d-block respectively).

Given the above, the most reasonable thing to do is to unset the height override, but this presents another challenge since the #popup-next-badge container has a flex__center helper class which centers flex items on both main and cross axis resulting in:

Fortunately, this is solved with the help of justify-content rule set to start (with !important as Stacks helper class also uses the rule) on the .popup._badge-selection container. Note that the inner js-badge-list-container needs another override back to center if you want the badges to be horizontally centered.

If you feel that it gets a bit too spacey when there are only one or two badges, a min-width rule on ._list-item class set to 256px or higher will help. In the end, you should get a result similar to this (for the ruleset summary see the short answer):